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Part BCSIR NET December 2023adjusted-r-squared

Adjusted r squared

Consider Y=α+βx+εY = \alpha + \beta{}x + \varepsilon with E(ε)=0E(\varepsilon) = 0. From 10 observations the OLS fit is ŷ = 1.5 + 0.8x. Suppose ∑(yi−\sum(y_{i} - ȳ)2=5)^{2} = 5 and ∑(xi−xˉ)2=6\sum(x_{i} - {\bar{x}})^{2} = 6. The adjusted R2(R^{2} (to two decimals) equals

  1. A.0.74✓ Correct
  2. B.0.83
  3. C.0.77
  4. D.0.84

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The trap it tests

Execution slip

The idea was right. The computation was not.

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Related counterexample: OLS is the BLUE in every linear model

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The chapter behind this: Linear models, Gauss–Markov and ANOVA — free to read

From Linear Models and Multivariate › Gauss–Markov, regression, ANOVA basics

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